I want to find the probability that X_i=1 and X_(i+1) = 2 for 500 (independent) rolls of an unfair 6-sided die with probabilities (.1, .3, 1, .2, .1, .2). I think it's just .1 * .3 but I'm not sure whether the answer depends on i (like if you just rolled the 500th roll or something like that) or on the number of rolls (like if we did 300 rolls instead of 500)? Can someone clarify this?

Sep 30th 2009, 11:15 PM

mr fantastic

Quote:

Originally Posted by horan

I want to find the probability that X_i=1 and X_(i+1) = 2 for 500 (independent) rolls of an unfair 6-sided die with probabilities (.1, .3, 1, .2, .1, .2). I think it's just .1 * .3 but I'm not sure whether the answer depends on i (like if you just rolled the 500th roll or something like that) or on the number of rolls (like if we did 300 rolls instead of 500)? Can someone clarify this?

What are X_i and X_(i+1)? Are they the number of spots on the ith roll and the (i+1)th roll?

Oct 1st 2009, 11:00 PM

CaptainBlack

Quote:

Originally Posted by horan

I want to find the probability that X_i=1 and X_(i+1) = 2 for 500 (independent) rolls of an unfair 6-sided die with probabilities (.1, .3, 1, .2, .1, .2). I think it's just .1 * .3 but I'm not sure whether the answer depends on i (like if you just rolled the 500th roll or something like that) or on the number of rolls (like if we did 300 rolls instead of 500)? Can someone clarify this?

A pair of consecutive rolls are to be assumed independent and the probability of each possible outcome on a roll is a constant, so the answer does not depend on i.